Scintillation index and bit error rate of hollow Gaussian beams in atmospheric turbulence

Based on the Huygens-Fresnel principle and Rytov method, the on-axis scintillation index is derived for hollow Gaussian beams (HGBs) in weak turbulence. The relationship between bit error rate (BER) and scintillation index is found by only considering the effect of atmosphere turbulence based on the probability distribution of intensity fluctuation, and the expression of the BER is obtained. Furthermore, the scintillation and the BER properties of HGBs in turbulence are discussed in detail. The results show that the scintillation index and BER of HGBs depend on the propagation length, the structure constant of the refractive index fluctuations of turbulence, the wavelength, the beam order and the waist width of the fundamental Gaussian beam. The scintillation index, increasing with the propagation length in turbulence, for the HGB with higher beam order increases more slowly. The BER of the HGBs increases rapidly against the propagation length in turbulence. For propagating the same distance, the BER of the fundamental Gaussian beam is the greatest, and that of the HGB with higher order is smaller.